Let $$ be an array of size $>=1,$ and $0<=<.[]=0[]=1.$ Decide which number $(01)$ is the

majority in $$ without counting their quantities.

Write a program named $$ in our language that can solve the above problem and bind the majority

among $0$ and $1$ to variable $.$ You can assume that $$ is written in the memory state; and to simplify the

question, we artificially define $[]=100,$ so you don$$t need to worry about a possible runtime error when the

array index reaches $.$ Your program doesn$$t have to be deterministic. Be careful of the grammar in our

programming language.

Here are some hints:

$1)$ We can use the following linear$-$search$-$like algorithm: scan the array $$ to pair up each $0$ with a $1.$ Once we

have some $1$ left over, then $1$ is the majority; once we have some $0$ left over, then $0$ is the majority; if

we can pair up all numbers, then either of them can be the majority.

$2)$ A student Jason wrote a partial solution that can be useful to solve the above problem:

$[0]=1->00+1[1]=0->11+1$

Consider $0$ and $1$ as pointers for number $0$ and $1$ respectively. What program $$ does is to find the next

$0$ and $1$

such that $[0]=0$ and $[1]=1.$ You can use $$ inside of your program.